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Martin H. Prior * Formalisation of Aspect: Further Work
36th Linguistic Colloquium, University of Ljubljana, 12th-14th September, 2001

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Towards a 'Differential Predicate Calculus'?

This page provides the Abstract for the above paper and an adaptation of the associated handout for the web. It further links (here and elsewhere) to a general bibliography on Time and Aspect. The paper will eventually be published in Proceedings of the 36th Linguistic Colloquium, held at the Faculty of Philosophy, University of Ljubljana, Slovenia, 12th-14th September, 2001.

Colloquium Site self on right

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ABSTRACT In a paper given two years ago to the 34th Linguistic Colloquium at Mainz on the The Formal Representation of Aspect, I outlined a model adapting Davidson's Theory of Action to Priorean Tense Logic. My adaptation of the Davidsonian model separated out actions and processes where the process separated out a change or continuation in the state of an object. Thus we might have P dt($ Q) (Arriving(Q) Ù Object (Q, x)) 'x arrived at time dt' Now I used dt and dt to capture points of time and intervals of time respectively, and I would like to extend the use of d/d to actions and processes themselves. Thus the above formula for 'x arrived' might become P dt($ f) (Arriving(f) Ù df(x)) Here we capture change over time, relating  df  and dt, a little like df/dt. In this paper I would like to look more closely at the properties of d and d with respect to both time references and actions and processes. It is this model I shall presume to call 'Differential Predicate Calculus'.

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HANDOUT

0.

The following formula re-caps the representation of the simple past from previous work.

P ^du ($ Q) (H _{d u}* ($ A) (P* Agent(x, A) Ù Kicking(A,Q)) Ù [Telic Operator] Compl Object (Q, y)
Ù Through (Q, z)))

x kicked the ball (y) through the goal-posts (z)
(qv. Tense operators)

 

1a. du = ~u Ù F ₊₀ u               1b. cu = u Ù P _-0 ~u

 

Numeric uses y = f(x) y + d y = f(x +d x) d y = f(x +d x) - y y - g y = f(x -g x) g y = y - f(x -g x)

Uses conjectured for logical form

2a. d u  É  du0 Ú du1 2b. d u  É  du0 Ú d u1 2c. d u  É  du0 Ú du1

3a. g u  É  cu1 Ú cu0 3b. g u  É  g u1 Ú cu0 3c. g u  É  g u1 Ú g u0

 

 

 

4.